101.[sinaxsin bxdx 1 -sin(a+b)x+2(a-b) 1 -sin(a-b)x +C 102.cosax cos bxdx= 1一sina+br+2a-b° 2(a+b) 1,sin(a-b)x+C X dx 2 atan~+b 103. arctan 2 +C(a2>b2) a+bsinx a2-b2 Va-b2 dx 1 atan'+b-√6-a 104.」 In +C(a2<b2) Ja+bsinx b2-a2 atan*+b+b-a 105.a+bcosx dx 2 a+b a-b arctan(, a+bVa-b tan)+C(a2>b2) a+b a+b tan dx 1 a+bIn 106.J a+bcosx a+616-1 2 b-a +C(a2<b2) a+b tan- 2 Vb-a dx 1 107.∫cos+6 sin'x ab b arctan(-tanx)+C a dx _=1 In btanx+a cos'x-b sin'x2abbtanx-a 108. +C 109. ∫sinadx=sinx-。xC054+-C a 110.[x'sinaxdx=-xcosax+ 2 2 xsinax+ a a cosax+C 1 1 1.[xcoscdosin+C a 112.x cosaxdxsixco 2 sinax+C a (十二)含有反三角函数的积分(其中a>0) 1l3.∫arcsin'dr=xaresin'+√2-x+C a a101. sin sin d ax bx x = 1 1 sin( ) sin( ) 2( ) 2( ) a b x a b x C a b a b 102. cos cos d ax bx x = 1 1 sin( ) sin( ) 2( ) 2( ) a b x a b x C a b a b 103. d sin x a b x = 2 2 2 2 tan 2 2 arctan x a b C a b a b 2 2 ( ) a b 104. d sin x a b x = 2 2 2 2 2 2 tan 1 2 ln tan 2 x a b b a C x b a a b b a 2 2 ( ) a b 105. d cos x a b x = 2 arctan( tan ) 2 a b a b x C a b a b a b 2 2 ( ) a b 106. d cos x a b x = tan 1 2 ln tan 2 x a b a b b a C a b b a x a b b a 2 2 ( ) a b 107. 2 2 2 2 d cos sin x a x b x = 1 arctan( tan ) b x C ab a 108. 2 2 2 2 d cos sin x a x b x = 1 tan ln 2 tan b x a C ab b x a 109. x ax x sin d = 2 1 1 sin cos ax x ax C a a 110. 2 x ax x sin d = 2 2 3 1 2 2 x ax x ax ax C cos sin cos a a a 111. x ax x cos d = 2 1 1 cos sin ax x ax C a a 112. 2 x ax x cos d = 2 2 3 1 2 2 x ax x ax ax C sin cos sin a a a (十二)含有反三角函数的积分(其中 a 0 ) 113. arcsin dx x a = 2 2 arcsin x x a x C a